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The Gerber-Shiu function for the compound Poisson Omega model with a three-step premium rate

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  • Zhongqin Gao
  • Jingmin He

Abstract

The compound Poisson Omega model is considered in the presence of a three-step premium rate. Firstly, the integral equations and the integro-differential equations for the Gerber-Shiu expected discounted penalty function are derived. Secondly, the integro-differential equations for the Gerber-Shiu expected discounted penalty function are determined in three different initial conditions. The results are then used to find the bankruptcy probability. Finally, the special cases where the claim size distribution is exponential be discussed in some detail in order to illustrate the effect of the model with three-step premium rate.

Suggested Citation

  • Zhongqin Gao & Jingmin He, 2019. "The Gerber-Shiu function for the compound Poisson Omega model with a three-step premium rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(24), pages 6019-6037, December.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:24:p:6019-6037
    DOI: 10.1080/03610926.2018.1524488
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